Google's John Mueller was asked if Google would add to Google Discover traffic a referrer that shows that click as coming from Google Discover versus Google search. John said no, Google has no plans on doing that.
He said you can get to the data within Google Search Console's Discover reports. Those Discover reports are awesome but yea, it would be nice to see Discover traffic from a referrer so you can do more with it in your own analytics.
Here are the tweets:
AFAIK there are no plans to break that out further -- that's what the Search Console reports should be for.
— 🍌 John 🍌 (@JohnMu) October 30, 2019
For now, you can 100% use those amazing Google Discover performance reports in Search Console. That is if you do get Google Discover traffic.
Forum discussion at Twitter.